Po-Shen Loh is a mathematician at CMU and coach of the USA International Math Olympiad team. Please support this podcast by checking out our sponsors:
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EPISODE LINKS:
Po's Twitter: https://twitter.com/poshenloh
Po's Website: https://www.poshenloh.com/
Daily Challenges: https://daily.poshenloh.com/
NOVID: https://www.novid.org/

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OUTLINE:
0:00 - Introduction
1:43 - Planes and bridges
5:21 - Writing a computer game from scratch
7:46 - Programming competitions
11:21 - Math is hard
16:52 - Contact tracing that preserves privacy
54:09 - Math Olympiad
1:09:49 - Hard math problem
1:17:06 - Is math discovered or invented?
1:22:02 - Intelligence
1:28:52 - Math education
1:33:03 - How to learn math
1:41:58 - Combinatorics
1:45:05 - Voting trees
1:55:29 - Stochastic coalescence
2:05:15 - P=NP
2:09:32 - Tolkien and WWII
2:11:52 - Advice for young people
2:13:57 - Meaning of life

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The following is a conversation with Po Shen Lo, a professor of mathematics at Carnegie Mellon University, national coach of the USA International Math Olympia Team, and founder of XP, that does online education of basic math and science.

He's also the founder of Novid, an app that takes a really interesting approach to contact tracing, making sure you stay completely anonymous, and it gives you statistical information about COVID cases in your physical network of interactions.

So you can maintain privacy, very important, and make informed decisions.

In my opinion, we desperately need a solutions like this in early 2020.

And unfortunately, I think we will again need it for the next pandemic.

To me, solutions that require large scale, distributed coordination of human beings, need ideas that emphasize freedom and knowledge.

Quick mention of our sponsors Jordan Harbinger show, Onnit, BetterHelp, 8sleep and element.

Check them out in the description to support this podcast.

As a side note, let me say that Po and I filmed a few short videos about simple, beautiful math concepts that I will release soon.

I really enjoyed Po sharing his passion for math with me in those videos.

I'm hoping to do a few more short videos in the coming months that are educational in nature on AI, robotics, math, science, philosophy, or if all else fails, just fun snippets into my life on music, books, martial arts, and other random things, if that's of interest to anyone at all.

This is the Lex Figman Podcast, and here's my conversation with Poe Shenlo.

You know, you mentioned you really enjoy flying and experiencing different people in different places.

There's something about flying for me, I don't know if you have the same experience, that every time I get on an airplane, it's incredible to me that human beings have actually been able to achieve this.

And when I look at what's happening now with humans traveling out into space, I see it as all the same thing.

It's incredible that humans are able to get into a box and fly in the air and safely and land.

And the same, it seems like, and everybody's taking it for granted.

So when I observe them, it's quite fascinating because I see that cleanly mapping to the world where we're now in rockets and traveling to the moon, traveling to Mars, and at the same kind of way, I can already see the future, where we will all take it for granted.

So I don't know if you have, you personally, when you fly, have the same kind of magical experience of like how the heck did humans actually accomplish this?

So I do, especially when there's turbulence, which is, you know, like on the way here, there was turbulence and the plane jiggled, even the flight attendant had to hold on to the side.

And I was just thinking to myself, it's amazing that this happens all the time and the wings don't fall off, you know, like given how many planes are flying.

But then I often think about it and I'm like, you know, a long time ago, I think people didn't trust elevators in a 40 story building in New York City.

And Now we just take it completely for granted that you can step into this shaft, which is 40 floors up and down, and it will just not fail.

Yeah, again, I'm the same way with elevators, but also buildings.

When I'll stand on the 40th floor and wonder how the heck are we not falling right now?

Like how amazing it is with the high winds, like structurally just the earthquakes and the vibrations.

I mean, natural vibrations in the ground.

Like how is this, how are all of these, you go to like New York City, all of these buildings standing.

I mean, to me, 1 of the most beautiful things, actually mathematically too, is bridges.

I used to build bridges in high school from like toothpicks, just like out of the pure joy of like physics making some structure really strong.

Understanding like from a civil engineering perspective, what kind of structure will be stronger than another kind of structure, like suspension bridges.

And then you see that at scale, humans being able to span a body of water with a giant bridge.

And it's, I don't know, it's so humbling.

It makes you realize how dependent we are on each other.

Sort of, I talk about level up, but there's a certain element in which we little ants have just a small amount of knowledge about our particular thing.

And then we're depending on a network of knowledge that other experts hold.

And then most of our lives, most of the quality of life we have has to do with the richness of that network of knowledge, of that collaboration, and then sort of the ability to build on top of it.

You start from bits in a computer, then you can have assembly, then you can have C++, or you have an operating system, then you can have C++ and Python, finally some machine learning on top.

And eventually we'll have AI that runs all of us humans.

But anyway, but speaking of abstractions and programming, in high school you wrote some impressive games for MS-DOS.

I got a chance to, in browser somehow, it's magic, I got a chance to play them.

What's the hardest part about programming those games?

And maybe can you tell the story about building those games?

I actually tried to do those in high school because I was just curious if I could.

That's a good starting point for anything, right?

But the appealing thing was also, it was a soup to nuts kind of thing.

So something that has always attracted me is I like beautiful ideas.

I like seeing beautiful ideas, But I actually also like seeing execution of an idea all the way from beginning to end in something that works.

So for example, in high school, I was lucky enough to grow up in the late 90s when even a high school student could hope to make something sort of comparable to the shareware games that were out there.

Not, I say the word sort of, like still quite far away, but at least I didn't need to hire a 3D CG artist.

There weren't enough pixels to draw anyway, even I can draw, right?

But the point is, I wanted to know, is it possible for me to try to do those things where back in those days, you didn't even have an easy way to draw letters on the screen in a particular font.

So for example, back then, if you played those games in the web browser, which is emulating the old school computer, those, even the letters you see, those are made by individual calls to draw pixels on the screen.

So you built that from scratch, almost building a computer graphics library from scratch?

The primitive that I got to use was some code I copied off of a book in assembly of how to put a pixel on a screen in a particular color.

The first 1 was in Pascal, but then The other ones were in C++ after that.

How's the emulation in the browser work, by the way?

to play these games that have a very much 90s feeling to them.

Ah, so it's literally making an MS-DOS environment, which is literally running the old .exe file.

This is, that could be more amazing than the airplane.

So it wasn't so much about the video games.

It was more about, can you build something really cool from scratch?

And you did a bunch of programming competitions.

What was your interest, your love for programming?

What did you learn through that experience?

Especially now that much of your work has taken a long journey through mathematics.

I think I always was amazed by how computers could do things fast.

If I wanted to make it an abstract analysis of why it is that I saw some power in the computer, because if the computer can do things so many times faster than humans, where the hard part is telling the computer what to do and how to do it, if you can master that, asking the computer what to do, then you could conceivably achieve more things.

And those contests I was in, those were the opposite in some sense of making a complete product, like a game is a product.

Those contests were effectively write a function to do something extremely efficiently.

And if you are able to do that, then you can unlock more of the power of the computer.

But also doing it quickly, There's a time element from the human perspective to be able to program quickly.

There's something nice, so there's almost like an athletics component to where you're almost like an athlete seeking optimal performance as a human being trying to write these programs.

And at the same time, it's kind of art because the best way to write a program quickly is to write a simple program.

So it's not necessarily you have to type fast.

You have to think through a really clean, beautiful solution.

I mean, what do you think is the use of those programming competitions?

Do you think they're ultimately something you would recommend for students, for people interested in programming or people interested in building stuff?

Yes, I think so because especially with the work that I've been doing nowadays, even trying to control COVID, something that was very helpful from day 1 was understanding that the kinds of computations we would want to do, we could conceivably do on like a 4 core cloud machine on Amazon Web Services out to a population which might have hundreds of thousands or millions of people.

The reason why that was important to have that back of the envelope calculation with efficient algorithms is because if we couldn't do that, then we would bankrupt ourselves before we could get to a big enough scale.

If you think about how you grow anything from small to big, if in order to

grow it from small to big, you also already need 10,000 cloud servers, you'll never get to big.

And also the nice thing about programming competitions is that you actually build a thing that works.

So you finish it, there's a completion thing and you realize, I think there's a magic to it where you realize that it's not so hard to build something that works.

To have a system that successfully takes in inputs and produces outputs and solves a difficult problem and that directly transfers to building a startup essentially that can help some aspect of this world, as long as it's mostly based on software engineering.

Things get really tricky when you have to manufacture stuff.

That's why people like Elon Musk are so impressive that it's not just software.

It's like you have to actually have factories that build cars and there's like a million components involved in the machinery required to assemble those cars and so on.

But in software, 1 person can change the world, which is incredible.

But on the mathematics side, what, if you look back, or maybe today, what made you fall in love with mathematics?

For me, I think I've always been very attracted to challenge, as I already indicated with writing the program.

I guess if I see something that's hard or supposed to be impossible, sometimes I say, Maybe I want to see if I can pull that off.

And with the mathematics, the math competitions presented problems that were hard, that I didn't know how to start, but for which I could conceivably try to learn how to solve them.

So, I mean, there are other things that are hard, called like, get something to Mars, get people to Mars.

And I didn't, and I still don't think that I'm able to solve that problem.

On the other hand, the math problems struck me as things which are hard and with significant amount of extra work, I could figure it out.

And maybe they would actually even be useful.

Like that mathematical skill is the core of lots of other things.

Maybe you could speak to that because a lot of people say that math is hard as a kind of negative statement.

It always seemed to me a little bit like that's kind of a positive statement.

That all things that are worth having in this world, they're hard.

I mean, everything that people think about that they would love to do, whether it's sports, whether it's art, music, and all the sciences, they're going to be hard if you want to do something special.

So is there something you could say to that idea that math is hard?

Should it be made easy or should it be hard?

Ah, so I think maybe I want to dig in a little bit onto this hard part and say, I think the interesting thing about the math is that you can see a question that you didn't know how to start doing it before.

And over a course of thinking about it, you can come up with a way to solve it.

And so you can move from a state of not being able to do something to a state of being able to do something where you help to take yourself through that instead of somebody else spoon feeding you that technique.

So actually here I'm already digging into maybe part of my teaching philosophy also, which is that I actually don't want to ever just tell somebody here's how you do something.

I actually prefer to say, here's an interesting question.

I know you don't quite know how to do it.

I'm actually explaining another way that you could try to do teaching.

And I'm contrasting this to a method of watch me do this, now practice it 20 times.

I'm trying to say a lot of people consider math to be hard because maybe they can't remember all of the methods that were taught.

But for me, I look at the hardness and I don't think of it as a memory hardness.

I think of it as a, can you invent something hardness?

And I think that if we can teach more people how to do that art of invention in a pure cognitive way, not as hard as the actual hardware stuff, right?

But like in terms of the concepts and the thoughts and the mathematics, teaching people how to invent, then suddenly, actually they might not even find math to be that tiresomeness hard anymore,

but that rewardingness hard of I have the capability of looking at something which I don't know what to do and coming up with how to do it.

I actually think we should be doing that, giving people that capability.

So hard in the same way that invention is hard, that is ultimately rewarding.

So Maybe you can dig in that a little bit longer, which is, do you see basically the way to teach math is to present a problem and to give a person a chance to try to invent a solution without with minimal amount of information first?

Is that basically how do you build that muscle of invention in a student?

Yes, so the way that, I guess I have 2 different sort of ways that I try to teach.

Actually, 1 of them is, in fact, this semester, because all my classes were remotely delivered.

I even threw them all onto my YouTube channel.

So you can see how I teach at Carnegie Mellon.

But I'd often say, hey, everyone, let's try to do this.

And That actually changes my role as a professor from a person who shows up for class with a script of what I want to talk through.

The way I show up for class is there's something that we want to learn how to do and we're going to do it by improv.

I'm talking about the same method as improv comedy, which is where you tell me some ideas and I'll try to yes and them.

And then together, we're gonna come up with a proof of this concept where you were deeply involved in creating the proof.

Actually, every time I teach the class, we do every proof slightly differently because it's based on how the students came up with it.

And that's how I do it when I'm in person.

I also have another line of courses that we make that is delivered online.

Those things are where I can't do it live, But the teaching method became also similar.

It was just, here's an interesting question.

And then automatic hints, we feed automatically hints through the internet to go and let the person try to invent.

So that's like a more rigorous prodding of invention.

But you did mention disease and COVID, and you've been doing some very interesting stuff from a mathematical but also software engineering angle of coming up with ideas, it's back to the, I can, I see a problem, I think I can help?

Can you tell me about your work there under the flag of Novid and both the software and the technical details of how the thing works.

So first I want to make sure that I say, this is actually team effort.

I happen to be the 1 speaking, but there's no way this would exist without an incredible team of people who inspire me every day to work on this, but I'll speak on behalf of them.

So the idea was indeed that we stepped forward in March of last year, when the world started to become, our part of the world started to become, our part meaning the United States started to become paralyzed by COVID.

And at that time, it started as a figment of an idea, which was network theory, which is the area of math that I work in, could potentially be combined with smartphones and some kind of health information, anonymized.

And many months into this work, we ended up accidentally discovering a new way to control diseases, which is now what is the main impetus of all of this work, is to take this idea and polish it and hopefully have it be useful not only now, but for future pandemics.

Actually, My main thing in the world is I come up with obvious observations.

Einstein did the same thing and he wrote a few short papers.

If we describe how usually people control disease for a lot of history.

It was that you'd find out who was sick, you'd find out who they have been around, and you try to remove all of those people from society against their will.

The against their will part gives you the wrong kind of a feedback loop, which makes it hard to control the disease, because then the people you're trying to control keep getting other people sick.

You can see already how I'm thinking and talking about this feedback loops.

This is actually related to something you said earlier about even like how skyscrapers stay in the air.

You actually want to, or even how an airplane stays, you need to have control loops which are feedbacking in the right way.

And what we observed was that the feedback control loop for controlling disease by asking people to be removed from society against their will was not working.

It was running against human incentives and you suddenly are trying to control 7 billion, 8 billion people in ways that they don't individually want to necessarily do.

And this is inspired by the fact that at the core of our team were user experience designers.

That's actually, in fact, the first thing I knew we needed when we started was to bring user experience at the core.

But so, The idea was, suppose hypothetically there was a pandemic.

You would want a way to be able to live your life as much as possible and avoid getting sick.

Can we make an app to help you avoid getting sick?

Notice how I've just articulated the problem.

It is not, can we make an app so that after you are around somebody who's sick, you can be removed from society.

It's, can we make an app so that you can avoid getting sick?

That would run a positive, I don't know if I want to call it positive or negative, but it would run a good feedback loop.

The only problem is that you don't know who's sick, because especially with this disease, if I see somebody who looks perfectly healthy, the disease spreads 2 days before you have any symptoms.

That's where the network theory comes in.

What if we changed the paradigm and we said, whenever there's a sickness, tell everybody how many physical relationships separate them from the sickness.

The trivial idea was the distance between you and a disease is not measured in feet or seconds.

It's measured in terms of how many close physical relationships separate you, like these 6 degrees of separation, like LinkedIn.

It turns out that actually unlocks some interesting behavioral feedback loops, which, for example, let me now jump to a non-COVID example to show why this maybe could be useful.

Actually, we think it could be quite useful.

Imagine there was Ebola or some hemorrhagic fever.

Imagine it spread through contact, through the air, in fact, pretend.

It has high fatality rate, and as you die, you're bleeding out of every orifice.

So the question is, suppose that such a disease broke, who would want to install an app that would tell them how many relationships away from them this disease had struck?

In fact, almost, I don't want to say almost everyone, that's a very strong statement, but a very large number of

Like the more deadly and transmissible the disease, the stronger the incentive to install it in a positive sense, in the good feedback loop sense.

Because with COVID, it was not as deadly as potential pandemics could have been, viruses could have been.

So it's sometimes muddled with how we think about it.

If the virus was a lot more deadly, you want to create a system that has a set of incentives that it quickly spreads to the population where everybody is using it and is contributing in a positive way to the system.

Exactly, and actually that point you just made, I don't take credit for that observation.

There was another person I talked to who pointed out that it's very interesting that this feedback loop is even more effective when the disease is worse.

And that's actually not a bad characteristic to have in your feedback loop, if you're trying to help civilization keep running.

Yeah, it's a really, it's in this dynamic.

Like people figure out, they dynamically figure out how bad the disease is.

The more it spreads, and the deadlier it is as the people observe it, as long as the spread of information, like semantic information, natural language information, is closely aligned with the reality of the disease, which is a whole nother conversation, right?

Maybe we'll chat about that, how we sort of make sure there's not misinformation, whether there's accurate information, but that aside, okay, so this is a really nice property.

Right, And just going on on that, actually just talking more about what that could do and why we're so excited about it, it's that not only would people want to install it, what would they do?

If you start to see that this disease is getting closer and closer, we surveyed informally people, But they said, as we saw it getting closer, we would hide.

But now, you notice what this has just achieved.

The whole goal on this whole exercise was, you got the people who might be sick, and you got everyone else, set A and set B.

Set A is the people who might be sick, set B is everyone else.

And for the entirety of the past contact tracing approaches, you try to get set A to do things that might not be to their liking or their will, because that's removing them from society.

We found out that there's 2 ways to separate set A from set B.

You can also let the people at set B, at the fringe of set A, attempt to remove themselves from this interface.

Everyone was looking at A, we look at B and suddenly B is in their incentive to do so.

So there's a virus that jumps from human to human.

So there's a network sometimes called graph of the spread of a virus.

It hops from person to person to person to person.

And each 1 of us individuals are sitting or plopped into that network.

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Po-Shen Loh: Mathematics, Math Olympiad, Combinatorics & Contact Tracing | Lex Fridman Podcast #183